googol +‎ -plex. Like the word googol, googolplex was coined in 1920 by the nine-year-old Milton Sirrota (1911–1981), the nephew of American mathematician Edward Kasner (1878–1955). The word was first published and precisely defined in the book Mathematics and the Imagination (1940) by Kasner and fellow mathematician James R. Newman (1907–1966) (see the quotation below).

The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired. This is a description of what would happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have [Primo] Carnera a better mathematician than Dr. [Albert] Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number of zeros is a googol. A googolplex is much bigger than a googol, much bigger than a googol times a googol. A googol times a googol would be 1 with 200 zeros, whereas a googolplex is one with a googol of zeros. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way.

If the universe were packed solid with neutrons, say, so there was no empty space anywhere, there would still only be about 10128 particles in it, quite a bit more than a googol but trivially small compared to a googolplex.

The theoretical number of nucleic acids in DNA, Jack had heard centuries ago, was ten to the power of one hundred and twenty thousand. He couldn't even imagine a number that would hold the set of possible universes, meaning every possible state and position for every particle in every Planck time. Googolplex, he thought, 1 followed by a googol of zeroes: googolplex raised to the power of googolplex.

Inflationary theory suggests that the entirety of space is vastly larger. Quantum theory suggests that there are many different copies of space of the same basic kind as ours (same laws of physics). String theory further suggests that there may be many different kinds of space. This whole collection of googolplexes of galaxies within each of googolplexes of different spaces within each of googols of kinds of space makes up an enormously vast universe or multiverse.

In some unimaginable future, the universe will stretch so thin that the light from one galaxy would be unable to reach any other galaxy. Eventually, all the stars would burn out, and the universe would consist of the dead cinders of stars, black holes, and uncountable googolplexes of cubic light-years of cold, empty space.

To a mathematician, a googolplex is the figure 1 followed by a googol of zeroes (a googol being the figure 1 followed by a mere 100 zeroes). To a real-estate man, it's one infinitesimal parcel of a plot of land.

Competition among bidders eventually resulted in the discovery of the "Googolplex," a quantity supposedly as near to nothing as possible—one over one with countless zeros [as the size of the portion of land the bidder would accept as security for a tax lien]. This, however, was not the limit of minuteness. The "Googolplex of a Googolplex," or "Gee Gee" for short, became the common bid in the sale of City of Miami tax certificates. There has apparently been no authoritative determination of the effect of an outstanding Miami tax certificate […]